# Foreign Bond Returns - CFAI Question

in the CFAI 2010 mock exam there is a question regarding foreign bond returns, that i just can’t seem to understand the answer and was hoping someone could help. (its question 54 for anyone whose done it) Question is - Basically expected Local return is 8.5% 1year domestic Rf rate is 1.3% 1year foreign Rf rate is 4.6% Spot rate is 0.69domestic/1foreign 1year forward rate is 0.67domestic/1foreign question is if the foreign currency is fully hedged, the bonds expected return is - A)3.9% B)5.2% C)5.6% (for bonds) I would expect B as R(domestic) = R(local) + R(currency) As R currency is approx = i(domestic) - i(foreign) = 1.3 - 4.6 = -3.3% R(domestic) = 8.5 - 3.3 = 5.2% answer B however the correct answer is C the reason is R(currency) = (F - So) / So = 0.67 - 0.69 / 0.69 = -2.9% R(domestic) = 8.5 - 2.3 = 5.6% i’ve checked the books and apparently the two equations for bond currency return should equal each other, however in this case they don’t. I’m confused as to why they’ve used one equation over the other anyone. Any ideas?

The only one possible explanation I see is that if Forward rate is provided, than we should use this market rate (not calculated forward price with interest rates). Here is the case when market and calculated forwards are different.

It’s a trick question. They gave you the forward rate so you dont have to do the back of the envelope by taking the rate differential. And they should equal each other but interest rate parity is not always at parity.

It is tricky… I’ve also seen (Ft-F0)/S0 for the calculation on the hedge too… think SerGrey is right in this case. F derived with IRP may not always hold, so go with the market priced forward because that is the rate you are heding with.

hey guys, got it wrong, too! picked up B:( one question please that I ve been keeping asking for weeks now I saw somewhere in CFAI (don t remember whether it was within the books or in samples or in mocks whatever…) for the hedged return for foreign bonds, they apply: RFR domestic + (Return foreign - REF Domestic), if we apply here, we ll get 5.2 % which is B! any idea? thanks! M.

Discussed many times on this board. Do a search. In this case IRP does not hold, so can not apply the old Rd + (Foreign bond premium) formula. You have to apply the forward discount/ premium. Its in the CFAI text.

they are giving you the forward price available in the market. you need to use that if you’re hedging currency risk. you’d use the IRP relationship if they didn’t give you the fwd price.